When we owned our Class C, it came with a fully mounted spare and a lug nut wrench, but no jack. The one time I assisted someone replace a flat on a smaller Class C, the rims were partially rust welded together and was a serious pain to separate the two rims even with a long tire iron.
We had AAA Plus with RV when we owned the Hybrid TT and kept it with the Class C. We had 1 blow out of an inner dual in the 7 years we owned it and I was glad to wait for AAA to find someone to take care of it for us. We waited about 2 hours for AAA to find someone, mainly because they were trying to find someone that could tow the Motorhome to a safer place if the Motorhome was not in a safe place. The company that came out within 30 minutes of getting the call could not tow the Motorhome and had the tire swapped quickly. I guess AAA finally gave up on the tow requirement. Fortunately, the rims separated without issue.
For us, AAA is as much about how much money we save on discounts at Hotels, Campgrounds, restaurants, etc. and it is rare that a year goes by and the savings don't pay for the membership.
-Michael